"The National Party are out of ideas, out of excuses and soon they will be out of office," he thundered in the run-up to the Budget.

"There will be a brighter future but only when they and their Klingons on the starboard bow are gone," he said.

For those who remember Mr Peters' pre-1996 promise to unseat National and kick out Prime Minister Jim Bolger, it was a statement worth careful reading.

After 1996 he justified joining a coalition because, he said: "We did stop the National Government" by joining it.

This time he seems to have closed down most of the wriggle room. "Out of office" is "out of office", however you refine it.

If Mr Peters is ruling out a deal with National if he holds the balance of power, it has become more than just a political pirouette on the head of a pin after the Budget.

National's support, already beginning to soften in some polls, slid four percentage points to 47 in last weekend's One News Colmar Brunton survey - the first time it had been under 50 per cent in that poll for two years.

It is not clear how much was caused by the public relations disaster that was the Budget, or how much was just "poll noise". The next survey from TV3, due to be published this weekend, should make the picture clearer.

But National has precious little room to shed support, given the fine margin of the Government's victory in November.

Of course, at 47 per cent National is holding its 2011 election night support, but important elements of the landscape around it have changed.

Labour plus the Greens - the MMP Centre-Left bloc - was 46 per cent in the TVNZ poll against 38.5 per cent at the election. Arguably they have cannibalised the NZ First vote, which was down from 6.59 per cent to about 2 per cent. If Mr Peters wins back enough support to hold the balance of power it could be at the expense of the Centre-Left bloc. So the more things change the more they may stay the same.

But over on National's side of the fence, all is not the same.

ACT is in the truck on the way to the knackers' yard, and there is no clear road ahead for the Maori Party if Tariana Turia and Pita Sharples retire. That leaves Peter Dunne and the outside chance the Conservatives can top 5 per cent as National's best bets for support.

John Key's dominance as preferred prime minister is also waning, but at 48 per cent against 14 per cent for Labour's David Shearer he is still streets ahead.

That, however, opens an intriguing possibility for the pundits: that while Mr Key remains dominant he could lose office. (In Australia, opposition leader Tony Abbott's personal popularity is diving but he remains on course for an easy victory over Labor.)

It also underscores how National can ill afford the sort of post-Budget blues it is suffering over the reforms to staff- student ratios.

Education Minister Hekia Parata is floundering, and though she gets an A+ for staying on message in press conferences, she deserves a "not achieved" when it comes to addressing the question.

Her poor performance - including an initial lack of detail on affected schools - has taken the blame for the policy's unpopularity.

But that is not completely fair.

The idea of increased class sizes as a trade-off goes back a long way, and has beguiled National MPs and some officials for some time. Former education minister Anne Tolley in 2009 pulled the plug on a similar idea after initial support from senior ministers.

And Treasury secretary Gabriel Makhlouf clearly thought the track was ready for a rerun when he flagged the possibility of increased class sizes in his briefing to incoming ministers last year.

So while Ms Parata is clearly enthusiastic about the policy, the blame for its unpopularity should be spread more widely.

Reading the tea-leaves and identifying political risks, especially at Budget time, is a matter of collective responsibility. If Mr Key and his team missed the potential for this policy to blow up in their faces, they deserve to share the blame.

Alarm bells should have been sounding deafeningly at any suggestion teacher numbers would reduce or class sizes increase - and all for a paltry $43m in savings.

It has been doubly damaging for National because it has put teachers and their unions back on the front foot, after National had successfully driven a wedge between them and parents over national standards. Parents and their children's teachers are unequivocally in the same camp over this issue.

It is now down to Mr Key to step off the plane, on his return from Europe, and lance the boil.

Nothing short of a guarantee to at least maintain existing class ratios will silence the criticisms, which have moved from the staffroom into the living room.

Even so, the Budget still has the potential to mark the key turning point for the Government. But it would be a travesty if Ms Parata alone was the fall-gal.